Higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimization

DOI10.1007/s11590-009-0170-5zbMath1229.90261OpenAlexW2017666241MaRDI QIDQ1958646

Qi-Lin Wang, Sheng Jie Li, Kok Lay Teo

Publication date: 4 October 2010

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-009-0170-5

zbMATH Keywords

weakly efficient solutionset-valued maphigher-order optimality conditionnonconvex set-valued optimizationgeneralized higher-order contingent (adjacent) derivative

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Programming in abstract spaces (90C48)

Related Items (22)

Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives ⋮ On optimality conditions for quasi-relative efficient solutions in set-valued optimization ⋮ New higher-order strong Karush-Kuhn-Tucker conditions for proper solutions in nonsmooth optimization ⋮ On necessary optimality conditions with higher-order complementarity slackness for set-valued optimization problems ⋮ Second-order optimality conditions with the envelope-like effect for set-valued optimization ⋮ Generalized higher-order semi-derivative of the perturbation maps in vector optimization ⋮ Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization ⋮ Weak efficiency in multiobjective variational problems under generalized convexity ⋮ Second-order optimality conditions for set-valued optimization problems under Benson proper efficiency ⋮ Second-Order Optimality Conditions for Set-Valued Vector Equilibrium Problems ⋮ Duality for nonsmooth semi-infinite programming problems ⋮ Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization ⋮ Erratum to: higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimization ⋮ Higher-order optimality conditions and duality for approximate solutions in non-convex set-valued optimization ⋮ Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces ⋮ Calculus rules of the generalized contingent derivative and applications to set-valued optimization ⋮ A note on ``Higher-order generalized Studniarski epiderivative and its applications in set-valued optimization ⋮ Second-order optimality conditions in set-valued optimization via asymptotic derivatives ⋮ On generalized second-order proto-differentiability of the benson proper perturbation maps in parametric vector optimization problems ⋮ Optimization of boundary value problems for higher order differential inclusions and duality ⋮ Second-order composed contingent epiderivatives and set-valued vector equilibrium problems ⋮ Higher-order optimality conditions for set-valued optimization with ordering cones having empty interior using variational sets

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